Increased water changes and a full dose of salt will clear it up if it is a fungus. I personally don't like keeping salt in a tank long term as it allowed both bacteria/fungus and fish to build up a resistance to it so it is not as effective when you need it. If it is a fungus, you may have trouble treating it with just salt as a result but you should try that first.

If it is a tumor, and I have had bettas with tumor just like that on their fins, it is not in a vital organ and is most likely benign. He should live a normal life with it.

if it doesn't go away and doesn't increase it may be fine...
my little guy has a TINY white speck right at the back of his head that I saw appear a few weeks after I brought him home and it's been there ever since best I can tell. it never turned into anything though and doesn't seem to hurt or harm him in any way >< just kinda there x-x and yeah, at least it's on the tail, non vital :D

With the addition of more aquarium salt, whatever the weird white thing was disappeared. Now it just looks like a pinprick hole in his fin. He was very active this morning, flaring at his pellets before nomming them down and begging for more.